On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

Philippe Toint; Frank Callier

doi:10.1007/BF00933294

On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

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Résumé

A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.

langue originale	Anglais
Pages (de - à)	511-529
Nombre de pages	19
journal	Journal of Optimization Theory and Applications.
Volume	23
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/BF00933294
Etat de la publication	Publié - 1 déc. 1977

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10.1007/BF00933294

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title = "On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms",

abstract = "A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. {\textcopyright} 1977 Plenum Publishing Corporation.",

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AB - A convergent minimization algorithm made up of repetitive line searches is considered in ℝ. It is shown that the uniform nonsingularity of the matrices consisting of n successive normalized search directions guarantees a speed of convergence which is at least n-step Q-linear. Consequences are given for multistep methods, including Powell's 1964 procedure for function minimization without calculating derivatives as well as Zangwill's modifications of this procedure. © 1977 Plenum Publishing Corporation.

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On the uniform nonsingularity of matrices of search directions and the rate of convergence in minimization algorithms

Résumé

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ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

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